Problem: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$6.50$, and bags of cookies cost $$3.00$, and sales equaled $$34.50$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+3y = 34.5}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${6.5x + 3}{(x+2)}{= 34.5}$ Simplify and solve for $x$ $ 6.5x+3x + 6 = 34.5 $ $ 9.5x+6 = 34.5 $ $ 9.5x = 28.5 $ $ x = \dfrac{28.5}{9.5} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(3)}{ + 2}$ ${y = 5}$ You can also plug ${x = 3}$ into $ {6.5x+3y = 34.5}$ and get the same answer for $y$ ${6.5}{(3)}{ + 3y = 34.5}$ ${y = 5}$ $3$ bags of candy and $5$ bags of cookies were sold.